The Concept of Comonotonicity in Actuarial Science and Finance: Theory

50 Pages Posted: 26 Aug 2003 Last revised: 18 Jan 2015

See all articles by Jan Dhaene

Jan Dhaene

Katholieke Universiteit Leuven

Michel Denuit

Catholic University of Louvain

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

Abstract

In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.

Keywords: Asian option, dependency, comonotonic copula, cash-flow, annuity, convex order bounds

Suggested Citation

Dhaene, Jan and Denuit, Michel and Goovaerts, Marc and Kaas, Rob, The Concept of Comonotonicity in Actuarial Science and Finance: Theory. Insurance: Mathematics & Economics, Vol. 31, No. 1, pp. 3-33, 2002 , Available at SSRN: https://ssrn.com/abstract=302322 or http://dx.doi.org/10.2139/ssrn.302322

Jan Dhaene (Contact Author)

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Michel Denuit

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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